Detecting damage in a panel subjected to transverse loads and undergoing limit cycle oscillations and chaos is investigated. The panel is mounted on a rigid substructure at its ends, and interacts with an unsteady supersonic flow on one side, and with a quiescent flow on the other side. This aeroelastic system includes structural nonlinearity due to the coupling between stretching and bending for deflections of the order of magnitude of the panel thickness. Also, energy dissipation is modeled by accounting for aerodynamic damping in the system. The flow is modeled using third order piston theory which includes aerodynamic nonlinearities. Finally, two types of damage are considered in the panel: (i) a local reduction in the bending stiffness (which may occur in many damage scenarios, such as the cases where yielding occurs or a crack propagates in the material), and (ii) a loss of stiffness in the upstream and/or downstream mounting points of the panel. Multiple damages are detected based on a state space analysis of the attractor of the dynamics of the aeroelastic system. Most of the current studies of such problems are based on linear theories. In contrast, the results presented are obtained using nonlinear dynamics, and have the advantage of an increased accuracy. The sensitivity of the nonlinear system dynamics to parametric changes is shown to be an effective tool for structural health monitoring.